After a short historical review concerning measurements of the dielectric response of simple glass formers, we discuss the complex dielectric permittivity ε ̂ ν above and below the glass transition temperature, T g, which we investigated in the frequency range 10 −3 Hz<ν<10 9 Hz. (i) As a first group of glass formers (type A systems) glycerol and propylene carbonate, which do not show a β-process, were studied, and a complete line-shape analysis of ε ̂ ν is presented. The evolution of the high-frequency wing of the main relaxation ( α-process) is the most prominent spectral change while cooling and leads to an essentially constant loss at T< T g. This yields approximately a “1/ f noise” in the spectral density, which extends at least over 7 decades in frequency (10 −2 Hz<ν<10 5 Hz). (ii) Several glass formers exhibit a pronounced β-relaxation in addition to the α-process (type B systems). Of these we investigated the dielectrically rigid systems toluene and fluoroaniline, as well as propanol and polybutadiene. The high-frequency wing observed in type A systems seems to reoccur also in type B systems. A quantitative line-shape analysis is carried out including both processes by applying the Williams–Watts (WW) approach. Compiling several properties of the β-relaxation, that are generally observed, we give new arguments supporting Johari’s idea, that the β-process is an intrinsic property of supercooled liquids, although its relaxation strength may vary significantly among different glass formers. In some cases even no discernible β-process is observed (type A systems). Within the WW approach, we interpret the β-process as a local, spatially restricted reorientational process which precedes the α-relaxation. Above T g, its relaxation strength strongly increases with temperature indicating that the spatial restriction imposed on the β-process reorientation is released upon emergence of the α-process.